State Conditional Filtering

In many dynamical state estimation problems, not all the values that the state can take have the same importance; hence, missing to deliver an appropriate estimate has more severe consequences for certain state values than for others. In many applications, such important state values correspond to events that have low a priori probability to happen (e.g., unsafe situations or conditions that one tries to avoid by design). Provably, Kalman filtering techniques are inadequate to correctly estimate such rare events. In this paper, a new state estimation paradigm is introduced to build confidence regions that contain the true state value, whatever this value is, with a user-chosen probability. Among regions having this property, an algorithm is introduced that generates in a Gaussian setup the region that satisfies a minimum-volume condition.